[BruceZ]

[ QUOTE ]
If you want to know the exact probability that you will be cleaned out . (ie , left with 0)

Then you would need to solve this equation for r .

r=0.5 + 0.5^10*r^11

Now take r^50 to get the probability that you lose exactly 50 units .

[/ QUOTE ]

That equation implies that the only ways to lose a 1 unit bankroll are losing on the first play, or winning 10 in a row, and then losing an 11 unit bankroll. This isn't correct as these are not the only possibilities.